I am a permanent resident of USA. I am planning to visit Ukraine for tourism and I will stay for 17 days. Do I need a visa since I am a lawful permanent resident of USA?
The Ukrainian foreign ministry's visa information page doesn't mention any condition relating to US permanent residents. You will need a visa for this trip if people of your nationality require a visa to visit Ukraine.
You've indicated in the comments that you're a Colombian citizen. The visa requirements for foreigners page states for Colombian citizens:
Visa required except for DP, SP holders.
DP, SP holders may enter and stay in Ukraine without visa for up to 90 days
(DP and SP refer to diplomatic and service passports respectively).
Assuming that you have a standard civilian Colombian passport, you will need a visa.